A clustering approach to identify the time of a step change in Shewhart control charts

Abstract

Control charts are the most popular statistical process control tools used to monitor process changes. When a control chart indicates an out-of-control signal it means that the process has changed. However, control chart signals do not indicate the real time of process changes, which is essential for identifying and removing assignable causes and ultimately improving the process. Identifying the real time of the change is known as the change-point estimation problem. Most of the traditional methods of estimating the process change point are developed based on the assumption that the process follows a normal distribution with known parameters, which is seldom true. In this paper, we propose clustering techniques to estimate Shewhart control chart change points. The proposed approach does not depend on the true values of the parameters and even the distribution of the process variables. Accordingly, it is applicable to both phase-I and phase-II of normal and non-normal processes. At the end, we discuss the performance of the proposed method in comparison with the traditional procedures through extensive simulation studies.

A type-2 fuzzy-statistical clustering approach for estimating the multiple change points in a process mean with monotonic change

“…1 illustrates, another clustering method is introduced to change point estimation literature. In this regard, Ghazanfari et al [10] introduced a statistical-clustering approach to identify the time of step change in Shewhart control charts which is applicable to both normal and nonnormal processes in either phase-1 or 2. Their cluster settings subjected to the constraint that clusters can only contain adjacent samples.…”

“…Their cluster settings subjected to the constraint that clusters can only contain adjacent samples. In order to estimate change point, Ghazanfari et al [10] considered all possible positions of τ and assumed that the observations before τ to be in the in-control cluster and all the observations beyond it to be in the out-of-control cluster. They showed that their proposed can considered as effective as the other traditional methods and also better than them in some cases.…”

“…Alaeddini et al [3] introduced a fuzzy-statistical clustering for estimating change points in X charts with fixed and variable sample size in phase-2 applications. Their clustering, as the same of Ghazanfari et al [10], is a combination of possible in-and out-of control clusters. Based on this fact that in SPC the random variables inherit probability characteristics, Alaeddini et al [3] comprehend that the probability measure performs better than the other similarity measures.…”

Identifying the time of a step change in AR(1) auto-correlated simple linear profiles

“…While Samuel et al (1998a, b), Pignatiello and Samuel (2001), Ghazanfari et al (2008), Perry et al ( , 2007, Perry and Pignatiello (2005, Fahmy and Elsayed (2006), and Noorossana and Shadman (2009) proposed procedures to estimate the change point in the parameters of univariate distributions, Nedumaran et al (2000), Atashgar and Noorossana (2010), Niaki and Khedmati (2012, 2014a, and Sullivan and Woodall (2000) considered change-point estimations in the parameter vectors of multivariate distributions. However, in some applications, the quality of a process can be better characterized by a relationship between a response variable and one or more predictors.…”

Identifying the time of a step change in bivariate binomial processes

“…For example, Jann [4] developed an estimator for multiple changes using genetic algorithm or Ghazanfari et al [5] applied clustering method for change point estimation in Shewhart control charts, and Atashgar and Noorossana [6] used artificial neural network for this purpose.…”